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Neck fragmentation

time. Neck fragmentation. Semi-peripheral reactions: Fragmentation in a smaller region, but with larger cross section !. Possibility to better disantangle and/or correlate kinematical and thermodynamical features. Impact parameter dependence. E/A = 35 AMeV; b=6 fm. free cross sections.

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Neck fragmentation

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  1. time Neck fragmentation Semi-peripheral reactions:Fragmentation in a smaller region, but with larger cross section ! Possibility to better disantangle and/or correlate kinematical and thermodynamical features

  2. Impact parameter dependence E/A = 35 AMeV; b=6 fm free cross sections half free cross sections P=Nternary/Ntotal 124Sn+64Ni 112Sn+58Ni

  3. NECK FRAGMENTATION: CM Vz-Vx CORRELATIONS Large dispersion also along transversal, x, direction TLF 124Sn + 64Ni 35 AMeV <0 IMF PLF >0 Alignement + Centroid at Clear Dynamical Signatures !

  4. DEVIATIONSFROMVIOLASYSTEMATICS r - ratio of the observed PLF-IMFrelative velocityto the corresponding Coulombvelocity; r1- the same ratio for the pair TLF-IMF TheNeck-IMF is weakly correlated with both PLF and TLF V.Baran, M.Colonna, M.Di Toro NPA 730 (2004)

  5. Gating the reduced plot for light IMFs: (exp. data)

  6. BNV REDUCED VELOCITY PLOTS: (exp. data) Note: BNV model accounts only for the “prompt” component of IMF’s V. Baran et al. Nucl. Phys A730 (2004) 329 Chimera 124Sn+64Ni 35AMeV data, same E_loss selections

  7. Angular distributions: alignment characteristics Out-of-plane angular distributions for the “dynamical” (gate 2) and “statistical” (gate 1) components: these last are more concentrated in the reaction plane. plane is the angle, projected into the reaction plane, between the direction defined by the relative velocity of the CM of the system PLF-IMF to TLF and the direction defined by the relative velocity of PLF to IMF (Chimera data)

  8. Stochastic mean field (SMF) calculations b = 4 fm b = 6 fm b = 2 fm Pre-equilibrium emission Fragment formation Sn124 + Sn124, E/A = 50 MeV/A

  9. Frammentazione in sistemi ricchi di neutroni • Convalidare il meccanismo di frammentazione. Nuovi aspetti legati a transizioni di fase in sistemi • asimmetrici • Dedurre informazioni sul comportamento dell’energia • di simmetria in condizioni di densita’ diverse da quelle • normali (bassa densita’)

  10. Symmetry Energy Expansion around r0 Asy-stiff Esym(rB) (MeV) Pressure & compressibility Asy-soft 0 1 2 3 rB/r0 Pressure gradient

  11. Mean Field & Chemical Potentials symmetry part of the mean field neutron-proton chemical potentials neutron neutron proton proton stiff 124Sn “asymmetry” I = 0.2 soft

  12. Fragment isospin properties: the iso-distillation Asy-stiff Central collisions 124Sn+ 124Sn 50 AMeV: average asymmetry Asy-soft 25 % reduction

  13. Comparison of isotopic distributions with data Stochastic BNV calculations T.X.Liu et al., PRC69(2004) 124Sn+ 124Sn 50 AMeV: central collisions

  14. Semi-peripheral collisions Asy-stiff: neutron enrichment of light IMFs 124Sn+ 124Sn 50 AMeV: average asymmetry Isospin migration Asy-soft V.Baran et al., NPA703(2002)603 NPA730(2004)329

  15. Fe + Fe @ 47 AMeV Ni + Ni, @ 47 AMeV d IMF’s properties vs. alignement R.Lionti et al., PLB 625 (2005) 33

  16. Transverse velocity dependence of fragment asymmetry asy-soft asy-stiff Sn124 + Sn124, E/A = 50 MeV/A b = 6 fm n-rich / n-poor ratio

  17. Asymmetry distributions in velocity bins 0 < v_tra /c < 0.02 v_tra /c > 0.02 asy-stiff asy-soft 0<A<10 asy-stiff asy-soft

  18. Fragment isotopic distributions • P(δρn – δρp) ~ exp – [ (δρn – δρp)² / (f(ρ,T) ρ/V) ] • P(N,Z) ~ exp –{ [(N-Z)-(Nº-Zº)]² / (ρV f(ρ,T)) } = • exp –{ a(N-Z)²- bN-cZ} • b = (4(Zº/ Aº)² - 1) / σ ; c = (4(Nº/ Aº)²-1) /σ • Isoscaling analysis (Y2(N,Z)/Y1(N,Z)) : exp(α N + β Z) • α = 4 [ (Zº/ Aº)²1 - (Zº/ Aº)²2 ] / σ σ = f(ρ,T) (ρV)/Aº • f(ρ,T) ~ T / Esym(ρ)(ρV)/Aº < 1 • ρ is the density of the initial low density (unstable) system

  19. Isoscaling: a way to analyze isotopic distributions Z=1 Z=7 primary Central collisions final α = 4 [ (Zº/ Aº)²1 - (Zº/ Aº)²2 ]/σ² α exp = 0.35 T.X.Liu et al., PRC2004

  20. Extraction of Esym from isoscaling analysis α = 4 [ (Zº/ Aº)²1 - (Zº/ Aº)²2 ] / σ σ ~ f(ρ,T) f(ρ,T) ~ T / Csym(ρ) Isoscaling in AMD (anti-symmetrized molecular dynamics) calculations A.Ono et al.

  21. In conclusione …. • Segnali che indicano transizione di fase liquido-gas: • Espansione radiale (bassa densita’) + bassa temperatura • Curva calorica • Bimodalita’ • Calore specifico negativo • Distillazione di isospin • Segnali che supportano il meccanismo spinodale: • Tempi di frammentazione (100 fm/c) • Formazione di frammenti di taglia tipica (segnale che sopravvive • solo in alcuni eventi) • Buona corrispondenza fra le osservabili cinematiche dei frammenti • e proprieta’ legate a massa e N/Z descrizione corretta della • dinamica di frammentazione

  22. Competition between reaction mechanisms: fusion vs deep-inelastic a) -- soft b) -- stiff neutron-rich Elab = 30 Mev/A, b = 4 fm proton-rich M.Colonna et al., PRC57(1998)1410

  23. Binary vs ternary reactions (neck emission) Reactions at low energy: Elab < 10 MeV/A (SPIRAL2) TDHF calculations: Davies et al, PRC20(1979)1372 139 86 Kr + La, l=100 Elab = 710 MeV Dynamical emission of small clusters at mid-rapidity

  24. asy-stiff More dissipative neck dynamics with asy-stiff ! 132 64 Sn + Ni Elab = 10 MeV/A b = 7 fm, t = 500 fm/c asy-soft

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